Systems of Vlasov-Poisson type are kinetic models describing dilute plasma. The structure of the model differs according to whether it describes the electrons or positively charged ions in the plasma. In contrast to the electron case, where the well-posedness theory for Vlasov-Poisson systems is well established, the well-posedness theory for ion models has been investigated more recently. In this article, we prove global well-posedness for two Vlasov-Poisson systems for ions, posed on the whole three-dimensional Euclidean space $ \mathbb{R}^3 $, under minimal assumptions on the initial data and the confining potential.

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\begin{document}$ {\mathbb{R}}^3 $\end{document} 中离子 Vlasov-Poisson 系统的全局强解

Vlasov-Poisson 型系统是描述稀等离子体的动力学模型。模型的结构根据它是描述等离子体中的电子还是带正电的离子而有所不同。与 Vlasov-Poisson 系统的适定理论已经很好地建立的电子情况相反，最近对离子模型的适定理论进行了研究。在本文中，我们证明了两个 Vlasov-Poisson 离子系统的全局适定性，在整个三维欧几里得空间 $ \mathbb{R}^3 $ 上，在对初始数据和限制势的最小假设下。